Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r103021 = re;
        double r103022 = r103021 * r103021;
        double r103023 = im;
        double r103024 = r103023 * r103023;
        double r103025 = r103022 - r103024;
        return r103025;
}
↓
double f(double re, double im) {
        double r103026 = im;
        double r103027 = re;
        double r103028 = r103026 + r103027;
        double r103029 = r103027 - r103026;
        double r103030 = r103028 * r103029;
        return r103030;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot re - im \cdot im\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(re + im\right) \cdot \left(re - im\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(im + re\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019156 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))